In the Star Trek universe we do see recognition of some holidays - Federation Day, First Contact Day, and, of course, birthdays. When are they celebrated? Every planet has a different year, so do they go by the earth year? Year of the planet they're closest to? Does Kira celebrate a birthday every Bajoran year and O'Brien celebrate his birthday every Terran year? (Which could lead to them having coinciding birthdays some years and not others.) When people's ages are reported on personnel or medical forms, do they use a single standard or a relative one? (I'm 24 in earth years, but 15 on my home planet.) How about major events like holidays? How do they know when to celebrate Federation Day or the Bajoran Gratitude Festival?
In the TNG episode "Data's Day" there is a reference to the Hindu festival of lights celebration starting on that day. Considering this holiday's date is calculated using the Terran lunisolar calendar, (new moon in the Indian month of Ashvan) at least some holidays are determined with traditional methods. Below is Data's log entry:
Second Officer's personal log. This is the 1,550th day since the Enterprise was commissioned. Besides the arrival of T'Pel, events today include four birthdays, two personal transfers, the Hindu Festival of Lights, two chess tournaments, a school play and four promotions. An ordinary day.